We have a contact support form in customer community using a global action for Case Creation, I can not see the "run assignment rule" option in global action layout like we have at normal page layouts.
It happens to me before when sandbox is refreshed. Just one more thing to check on the case page layout of that record type. Go to layout Properties and make sure the default is checked for Case Assignment Checkbox.If it still doesn't work, check if off, save, then check it on and save it again.
There is an SF Idea post here - https://success.salesforce.com/ideaView?id=0873A00000159FNQAY and here - https://success.salesforce.com/ideaView?id=08730000000l5Z0AAI which is related to your post. Always worth a vote!